1) Giving PC to elements that is on par with the existing PC does not buff PC. If PC were buffed then shields would be nerfed. I cannot conclude that giving PC to elements that is on par with existing PC would nerf shields. (Completion and Balance are separate axises)
You have to include in the analysis of a card's power the likelihood of a card being in the enemy's deck which effectively counters the card. I do think that if 5 elements gained explosion, that you would see more use of explosion, and thereby, the power of permanents would be reduced globally. So I disagree with your statement that completion and balance are separate axises (unless you have a degenerate situation where everyone is forced to play a limited set of elements). However, as I said before, I agree that adding PC, soft or otherwise, to more elements, would be a great thing for the game.
2) Is the incompleteness of 5 elements good for the game? No. Can I conclude Dim Shield is the problem? No.
It's not *the* problem, it is one of many problems. But don't forget that completeness can only be defined in terms of cards that can shut down your deck if it is not complete. For example, if all non-pillar permanents were shard of void, then PC would not be a component of completeness.
3) "Dim Shield or those decks" is a false dichotomy.
I claim there exist many decks that would be viable if dim shield was eliminated, but are not currently viable (and I add that many of them are interesting). I will define viable as having a win percentage of 50% or greater in the PvP meta minus SoF. Perhaps I am wrong about that. But even the existence of one such deck would make it not a false dichotomy. But the burden is on you to demonstrate that there are no such decks before you can make a claim of a false dichotomy. You may find fault with my claim, but you can't dismiss it entirely (yet).